A176476 Partial sums of A012814.

0, 1, 6, 27, 113, 464, 1896, 7738, 31571, 128800, 525455, 2143647, 8745216, 35676948, 145547524, 593775045, 2422362078, 9882257735, 40315615409, 164471408184, 670976837020, 2737314167774, 11167134898975, 45557394660800, 185855747875875, 758216295635151

Offset

0,3

Comments

Old name was "a(n) is the minimum integer that can be expressed as the sum of n Padovan numbers (see A000931)".

Lim_{n -> infinity} a(n+1)/a(n) = p^5 = 4.0795956..., where p is the plastic constant (A060006).

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (6,-9,5,-1).

Formula

a(n) = A012855(n+3) - 1. a(n) = 6*a(n-1) - 9*a(n-2) + 5*a(n-3) - a(n-4). - R. J. Mathar, Oct 18 2010

G.f.: x/(1 - 6*x + 9*x^2 - 5*x^3 + x^4). - Colin Barker, Feb 03 2012

From Jianing Song, Feb 04 2019: (Start)

a(n+3) = 5*a(n+2) - 4*a(n+1) + a(n) + 1.

a(n) = Sum_{k=0..n} A012814(k) = Sum_{k=0..n} A000931(5*k+2). (End)

Example

a(5) = A000931(2) + A000931(7) + A000931(12) + A000931(17) + A000931(22) + A000931(27) = 0 + 1 + 5 + 21 + 86 + 351 = 464.

Prog

(PARI) a(n) = my(v=vector(n+1), u=[0, 1, 6, 27]); for(k=1, n+1, v[k]=if(k<=4, u[k], 5*v[k-1] - 4*v[k-2] + v[k-3] + 1)); v[n+1] \\ Jianing Song, Feb 04 2019

Crossrefs

Cf. A000931, A012814, A012855, A060006.

Sequence in context: A220101 A014825 A141844 * A079742 A291232 A171475

Adjacent sequences: A176473 A176474 A176475 * A176477 A176478 A176479

Keyword

nonn,easy

Author

Carmine Suriano, Apr 18 2010

Extensions

New name, more terms and a(0) = 0 prepended by Jianing Song, Feb 04 2019

Status

approved